Stir ¼ teaspoon of the black pepper into the mashed potatoes and set aside.

Heat the olive oil in a large skillet over medium heat. Add the diced onion and carrots and cook for approximately 4 minutes, stirring occasionally, until softened. Add the ground beef and cook until no longer pink, breaking it up as it cooks. Stir in the minced garlic.

Season the beef mixture with salt and the remaining black pepper. Add the Worcestershire sauce, garlic powder, onion powder, flour, water, and peas. Cook for approximately 2 minutes, stirring frequently, until the mixture thickens. Stir in the parsley and thyme. Remove from heat and allow to cool slightly.

Preheat the oven to 400°F (200°C). Roll the pie crusts to ⅛-inch thickness and cut into 4×3-inch rectangles, or alternatively 6×4-inch rectangles if folding over.

Place a spoonful of mashed potatoes onto the center of each rectangle, followed by a portion of the beef mixture, leaving a border around the edges. Lightly moisten the edges with water, then place a second rectangle on top or fold the dough over to enclose the filling. Press firmly along the edges to seal.

Transfer the hand pies to lined baking sheets. Brush the tops and edges with melted butter.

Bake for 25–30 minutes, or until the pastry is golden brown and fully cooked. Serve warm.